Synthesis, microstructural and optical characterizations of sol-gel grown gadolinium doped cerium oxide ceramics

In this study, through the utilization of the sol–gel combustion tactic, gadolinium (Gd)-doped cerium oxide (CeO2), Ce1−xGdxO2 (x = 0.00, 0.10, 0.20 and 0.30 (GDC)) ceramics were attained. The synthesized GDC ceramics were investigated using X-ray diffraction (XRD) to scrutinize their crystal structures and phase clarities. The obtained GDC ceramics have a single-phase cubic structure and belong to the crystallographic space group fm3̄m (225). The measurement of the diffraction angle of each reflection and the subsequent smearing of the renowned Bragg's relation provided coarse d-interplanar spacings. The stacking fault (SF) values of pure and Gd-doped CeO2 ceramics were assessed. To muse the degree of preferred orientation (σ) of crystallites along a crystal plane (h k l), the texture coefficient (Ci) of each XRD peak of GDC ceramics is gauged. By determining the interplanar distance (dh k l), the Bravais theory sheds light on the material's development. By exploiting Miller indices for the prime (1 1 1) plane, the lattice constants of GDC ceramics and cell volumes were obtained. Multiple techniques were employed to ascertain the microstructural parameters of GDC ceramics. A pyrometer substantiated the density of GDC ceramics. The room temperature (RT) Fourier transform infrared (FTIR) spectra of both un-doped and Gd-doped CeO2 were obtained. The UV-vis-NIR spectrometer recorded the GDC ceramics' reflectance (R) spectra at RT. For both undoped and Gd-doped CeO2, the absorption coefficient (α) spectra showed two distinct peaks. The R-dependent refractive index (η) and the α-dependent extinction coefficient (k) were determined for all GDC samples. The optical band gap (Eg) was obtained by integrating the Tauc and Kubelka–Munk approaches for GDC ceramics. For each GDC sample, the imaginary (εi) and real (εr) dielectric constants, as well as the dissipation factor (tan δ), were determined local to the characteristic wavelength (λc). Calculations were made for the Urbach energy (EU) and Urbach absorption coefficient (α0) for GDC ceramics. The minimum and maximum values of optical (σo) and electrical (σe) conductivity for GDC ceramics were determined. The volume (VELF) and surface (SELF) energy loss functions, which depend on the constants εi and εr, were used to measure electrons' energy loss rates as they travel across the surface. Raman spectroscopy revealed various vibrational modes in GDC ceramics. Finally, the implications are discussed herein.


Introduction
Several researchers have studied cerium oxide (CeO 2 ), and their verdicts cover an all-embracing gamut of potential uses.The rare earth oxide CeO 2 has a lot of latent applications in electrooptical devices, 1 optoelectronic devices, 2 and microelectronic devices. 3Therefore, it is indispensable to ne-tune the morphological and structural features of CeO 2 for diverse applications, such as photocatalysis, 4 gas sensors, 5 solar cells, 6 fuel cells, 7 polishing materials, 8 corrosion protection coating for all metals and alloys, 9 materials for superconductor electrodes in electrochemistry, and antibacterial medication.
The cubic uorite structure of cerium oxide is retained up to its melting point (x2700 K) and is chemically inactive toward most electrode materials.The ionic conductivity of CeO 2 is meager, making it inapt for fuel cell applications because of its low oxygen vacancy concentration.The conductivity can be enhanced by including aliovalent dopants such as Sm, Nd, Gd, Ca, Cu, and Pr in the cerium oxide. 10Gadolinium (Gd 3+ : 119.3 pm), whose ionic radius nearly resembles that of cerium oxide (Ce 4+ ; 111 pm), is the most oen used dopant in cerium oxide. 11xygen vacancies are created 12 due to Gd 3+ substitution in the cerium oxide lattice, which increases the electrolyte's ionic conductivity.Gadolinium-doped cerium oxide has a more excellent ionic conductivity than conventional yttria-stabilized zirconia at intermediate temperatures (775-975 K), making it a suitable replacement in solid oxide fuel cells in this temperature range.The temperature, defect dissociation, size of the dopant, the microstructure of sintered pellets, oxygen partial pressure, degree of doping, and sample preparation technique all hinder the ionic conductivity of gadolinium-doped cerium oxide. 13Highly dense ceramics must be synthesised because ionic conductivity is inuenced by the synthesis process and the ceramic's density.It is crucial to reduce the sintering temperature because ceramics composed of cerium oxide require high sintering temperatures (1875 K), which lengthen fabrication times and raise the cost of these ceramics.This temperature can be reduced by employing initial nano-sized powders.
As a result of its inherent limitations, no crystal can be considered awless; an ideal crystal would appear to extend innitely in every direction.Changes from highly crystallinity-preserving materials cause diffraction peak broadening.Crystallite size (D) and strain (3) are the main metrics derived from XRD peak width analysis.Several theoretical methods can be used to determine the average D and 3.These include the Debye Scherrer (D-S) method, Williamson-Hall (W-H) method with uniform deformation models, Size-Strain plot (SSP), and Halder-Wagner (H-W) method.
One of the most fascinating and advantageous features of semiconductors is their optical characteristics.Dispersion phenomena cause electromagnetic waves to lose energy as they travel, which makes the real component, called the refractive index (h), and the imaginary part, called the extinction coefficient (k), more complicated.It has been noted that the most precise ways to determine the energy gap (E g ) are by optical absorption (A) measurements. 14sing the sol-gel combustion process, this paper describes the production of gadolinium (Gd)-doped cerium oxide (CeO 2 ) and gives detailed information about the microstructural and optical properties of intrinsic and Gd-doped CeO 2 ceramics.It is anticipated that researchers worldwide will leverage results to sneak them into all sorts of devices.

Synthesis
The 4N untainted cerium(III) nitrate hexahydrate [Ce(NO 3 ) 3 -$6H 2 O] (Merck, Germany) and gadolinium(III) nitrate hydrate [Gd(NO 3 ) 3 $H 2 O] (Merck, Germany) were used as metal precursors to concoct powders of composition Ce 1−x Gd x O 2−d (x = 0.00, 0.10, 0.20 and 0.30, denoted as GDC-00, GDC-10, GDC-20, and GDC-30, respectively).3N untainted ethylene glycol [C 2 H 6 O 2 ] (Loba Chemie, India) and citric acid monohydrate [C 6 H 8 O 7 ] (Loba Chemie, India) were used for the polymerization process.The metal precursors were dissolved in double distilled water (DDW); the solution was then mixed with ethylene glycol and citric acid.The molar ratios of citric acid: metal oxide and citric acid: ethylene glycol were kept at 1 : 2 and 1 : 4, respectively.Aer 2.0 hours of sonication at a high frequency (20 kHz) and high power of 550 W with a 15 second on-off cycle, the mixture was subjected to a temperature of 65-75 °C and stirred on a hot plate to expedite gelation.The ensuing dark brown gel was then placed in an oven at 260 °C to activate auto incineration.The resulting ash-like substance was heated to 550 °C for 2.0 hours to eliminate organic excess.The calcinated powder was pressed at 110 MPa hydraulic pressure for pellet (10 mm diameter and 03 mm thickness) creation and sintered at 1500 °C for 6 h.

Characterization
The crystal structures of GDC ceramics were determined by X-ray diffraction (XRD) (model: X'Pert MPD; make: Philips, Holland) exploiting the typical CuKa radiation (x0.1541 nm) in the 2q range 20°to 90°.The densities of GDC ceramics were measured using a densitometer (model: Smart Pycno 30, make: Smart Instruments Company Pvt. Ltd., India).Fourier transform infrared (FTIR) spectroscopy (model: Spectrum-GX, make: Perki-nElmer, USA) was executed at room temperature (RT) (x303 K) in the wavenumber (n) range 4400-300 cm −1 to identify the functional groups extant in the synthesized GDC ceramics.A UV-vis-NIR spectrometer (model: Lambda 19, make: PerkinElmer, USA) was used to acquire the optical strictures of GDC ceramics.A micro-Raman apparatus (Model: STR 500 spectrometer) was used for conducting the RT Raman investigation on the GDC ceramics, which entailed stimulation at 532 nm in their vibrational mode.
The d-interplanar spacings were determined by gauging the diffraction angle of each reection according to the eminent Bragg's relation, eqn (1): The d-spacings for each reection are given in Table 1.
One crystallographic aw is the stacking fault (SF), which manifests as planar defects in two dimensions and indicates the incompetence of crystallographic planes.Table 1 shows the SFs of Gd-doped and pure CeO 2 for four broad peaks, as predicted by eqn (2): 16 Here, b is a measure of the full breadth/width at half maximum of the diffraction peak.
Utilizing eqn (3), one can discern the crystallites' preferred orientation along a crystal plane (h k l) by gauging the texture coefficient (C i ) of each XRD peak of GDC ceramics: 17 C i signies the texture coefficient of the plane i, I i symbolizes the integral intensity, I i0 designates the integral intensity of the reported data of the corresponding peak i; N, which is equal to 4 in this investigation, represents the number of reections in the X-ray diffraction pattern being examined.An irrationally oriented sample has a C i value of one for every reection; a value greater than one indicates the preferred orientation of the crystallites in that particular direction.
A determination of the GDC ceramics' degree of preferred orientation (s) can be made by calculating the standard deviation of all C i values using eqn (4): 17 The texture coefficient C i0 is scaled to 1, and s is the gauge of the sample's orientation; a value of zero evokes a random orientation, while a more excellent value of s proves a modied preferred orientation.Table 1 boasts access to the C i values of the four prominent peaks and the s value for GDC ceramics.
To gain insight into the evolution of the material, the Bravais theory was used to nd the distance (d h k l ) between the crystal planes.The theory propositions the related distance between crystal planes (d h k l ) and the growth rate of the plane (R h k l ) as A collection of lattice parameters (a, b, c, a, b, g) for the GDC crystal system can be used to compute the d h k l according to eqn (5): 18 It is possible to deduce the signicance of the GDC's (1 1 1) plane from the estimated d h k l , which unveils that d 1 1 1 is the greatest (Table 1), emphasizing that h 1 1 1 is the smallest.This is due to, according to Bravais theory, 18 the growth rate of the (1 1 1) plane R 1 1 1 being the smallest.
For the cubic crystal system, eqn (6) (ref.19) shows a relationship between the lattice parameter (a) and d-value for each Miller index.

Microstructural parameter analysis
It is crucial to research the properties of a compound before using it in contexts of cutting-edge technology.By examining its  19,20 Lattice strain is the internal stress that compresses or expands the length of a unit cell compared to its initial size.This article boasts a range of approaches to evaluating the microscopic structure of GDC.3.2.1.The Nelson-Riley (N-R) method.The N-R tactic, the error function, can be employed to determine the lattice parameter (a) of cubic GDC ceramics.To obtain the error function from eqn (7), the N-R graph was constructed by combining the computed lattice parameters from several planes: 21 2f ðqÞ ¼ cos 2 q sin q þ cos 2 q q (7) Table 2 displays the results, and Fig. 2 shows the N-R plot, where the intercept was utilized to determine a (where a = intercept).
The lattice parameters and volume computed for GDC are displayed in Table 2 Lattice parameter (a) values increased with increasing amounts of Gd-doped into the parent CeO 2 , as shown in Fig. 2. The conversion of specic fractions of Ce 4+ into Ce 3+ , a form of cerium with a greater ionic radius (1.14 Å compared to 0.97 Å for Ce 4+ ), could be a likely reason why the lattice parameter value increases when doped. 22.2.2.The Scherrer method.The Scherrer eqn (8) can be used to estimate D from the breadth/width of XRD lines: 19 Db cos q = Kl ( Scherrer's constant is denoted as K (x0.9).On rearranging eqn (8), we obtain eqn (9), Fig. 3(a) shows the Scherrer plot, and Table 3 provides the average D (=KlSlope).Table 3 does not include the D value for GDC-20 since the current experiment produced a D value greater than 200 nm, which is outside the range of validity for  Scherrer's computation, which is limited to average D values between 100 and 200 nm. 23There is a negative correlation between the size of a crystallite and its full width at half maximum (FWHM); therefore, when the parent CeO 2 is doped with Gd, the FWHM of all planes increases, leading to smaller crystallites.
3.2.2.1.The Stokes-Wilson (S-W) method.The lattice 3 predisposed by crystal imperfection and chaos was resolute in the un-doped and Gd-doped CeO 2 samples using the Stokes-Wilson (S-W) relation eqn (10): 24 3 ¼ b 4 tan q (10) Table 3 shows the average 3 (=Slope) speculated from the S-W plot (Fig. 3(b)), and it is that disparity in radii between the host cation (Ce) and the dopant (Gd) that stirs strain in the host lattice.
With the aid of the S-W relation eqn (11), it is possible to compute the micro-strain (3 rms ) along each mineralographic plane: 24 3 rms 2 = 0.643 2 Fig. 3(c) shows a plot of micro-strain (3) vs. root mean square strain (3 rms ), demonstrating that the crystallographic direction of the lattice planes is consistent.When plotted against an abscissa, the data points should form an angle of 45 degrees, indicating that 3 has a linear relationship with 3 rms . 25.2.3.The Monshi method.In their report, Rabiei et al. 26 conrmed that Scherrer's equation increased the projected nanocrystalline sizes for increasing 2q values.An example of how Monshi modied Scherrer's original formula is seen in eqn (12).27 ln The average D, which is equal to Kle Intercept −1 , was gured out in Fig. 3(d) and is accessible in Table 3.
3.2.6.The size-strain plot (SSP) method.According to the W-H scrutiny, the diffraction angle 2q portrays peak broadening as an aermath of the juxtaposed effects of D and 3 -induced broadening.
The SSP approach considers the XRD line analysis a combination of Lorentzian and Gaussian functions and uses eqn (15)  to compute D and 3: 30 D, which is equal to KlSlope −1 , and 3, which is equal to 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Intercept p , were obtained from the linear ts for GDC indicated in Fig. 5(a); the results can be found in Table 3.
3.2.7.The Halder-Wagner (H-W) method.The SSP method's XRD peak width assumption is false because neither the mid-peak area nor the XRD peak's tail could be mapped using the corresponding Gaussian nor Lorentzian functions.
Using the convolution of Gaussian and Lorentzian functions, we can debunk the H-W analysis's premise that peak broadening is the Voigt function.Eqn ( 16) and Fig. 5(b) illustrate the connection between D and 3 concerning the H-W technique: Here, b * ¼ b cos q l and d * ¼ 2 sin q l a Compressive stress, denoted by a negative 3 value for GDC, results from the assertion of equal and opposing pressures, which in turn causes the crystalline structure to shrink. 32,33g. 4 W-H plots (UDM) for GDC-00, -10, -20, and -30 ceramics.The straight line in plot 5 (b) gives D, which is equal to slope −1 , and 3 can be determined from the intercept (equal to 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Intercept p ).The results can be seen in Table 3.

Fourier transform infrared (FTIR) analysis
The RT FTIR spectra of un-doped and Gd-doped CeO 2 recorded in the 4400 to 300 cm −1 wavenumber (n) range are shown in Fig. 6.The un-doped CeO 2 (GDC-00) spectrum exhibited a higher absorbance intensity than the Gd-doped spectra (GDC-10, -20, and -30); the peaks below 700 cm The peaks between 1400-1500 cm −1 and 2350-2360 cm −1 are caused by carbonate-type species associated with oxide particle surfaces, such as ambient CO 2 , interacting with cerium cations to form species that would decompose following sample treatment at high temperatures. 34A study conducted by Aboud et al. 35 showed that Gd-doped CeO 2 gas sensors have improved sensitivity, stability, operating temperature, and the capacity to detect CO 2 gas.The doping effect of Gd in CeO 2 is pragmatic and occurs between 2350-2360 cm −1 .Residual water and hydroxy groups were indicated by a large band between 3600-3800 cm −1 , agreeing with the O-H stretching vibration and near 1600 cm −1 due to the bending vibration of the associated H-O-H water molecule.A minuscule peak at 731 cm −1 was observed in the CeO 2 spectrum but was not seen in the doped samples.As the doping concentration of Gd increased, the peak's intensity (absorbance) decreased, which may be due to the bending of Gd-O-Ce. 36,37

UV-vis-NIR spectroscopy analysis
Regarding denitive optical strictures, ultraviolet-visible-near infrared (UV-vis-NIR) spectroscopy is the way to go.Depending on the shape and properties of the material under examination, the optical spectra obtained from UV-vis-NIR spectroscopy can exist in several modes, such as transmittance (T), reectance (R), and absorption (A).The Tauc technique, which uses the absorption (A) and/or transmittance (T) spectra of UV-vis-NIR spectroscopy, can be used to estimate the band gap (E g ) of a transparent sample.On the other hand, a nontransparent sample has low transparency, oen approaching zero, and the E g can be determined from the diffuse reectance spectra (DRS).The current study used reectance mode UV-vis-NIR spectroscopy on GDC ceramics at RT in the l range of 200 to 2500 nm.As a function of l, Fig. 7 shows the R spectra, and GDC ceramics spectra were computed using the Kubelka-Munk (K-M) theory.The observed maximum l shis from x240 (11.23%R) to x370 (16.90% R) nm for GDC-00, x242 (16.58%R) to x388 (19.75% R) nm for GDC-10, x242 (18.24%R) to x377 (21.46%R) nm for GDC-20, and x239 (15.14% R) to x370 (18.16%R) nm for GDC-30, designate the establishment of CeO 2 (GDC-00) and Gd-doped CeO 2 (GDC-10, -20, and -30) due to the electron transition from O-2p to Ce-4f. 38or GDC ceramics, Fig. 8 shows how the optical parameters a (= FðRÞ t , where t (x3 mm) is the thickness of the GDC pellets),  A key feature of composite materials is the Rdependent h, which is strongly related to the electronic polarizability of ions and the local eld within the material; Fig. 8(b) shows that h was found to be x2.3961 at a l c (x370 nm) for GDC-00, x2.5998 at a l c (x388 nm) for GDC-10, x2.7261 at a l c (x378 nm) for GDC-20, and x2.4852 at a l c (x370 nm) for GDC-30, 39 and ties well with the empirical relation . 40 As l increases, h rises due to higher absorption at longer l. 41The absorption of electromagnetic waves in semiconductors because of inelastic scattering events is re-ected in the extinction coefficient (k), which is a measure of the fraction of light energy lost by scattering and/or absorption per unit distance of transit in a medium like ceramic.The value of k, which is directly proportional to a, 42  Combining the Tauc and K-M techniques, as shown in eqn (17), allows one to determine the optical E g of GDC ceramics: 43 The photon energy is denoted by hn, the transition probability is denoted by n, and A is a constant.Fig. 9 shows the plot of (ahn) 2 against hn, which is used to nd the optical E g of GDC ceramics.The direct optical E g value may be determined by extrapolating the straight section of the graphs at the values where (ahn) 2 = 0; the results for the direct E g for GDC ceramics are shown in Table 4.
There are two parts to the complex optical dielectric function: the imaginary (3 i ) and the real (3 r ) components; the former represents the absorption of energy from an electric eld because of dipole motion, and the latter represents the capacity of materials to reduce the speed of light; 3 i and 3 r have unswerving relationships with the h and k.Fig. 10 shows the relationship between energy and the changes in the imaginary dielectric constant (IDC) (3 i )(=2hk) (Fig. 10 The relationship between energy (E g ) (=hn) and the changes in ln a, optical conductivity (s o ), and electrical conductivity (s e ) are shown in Fig. 11.An alteration in the optical state occurs when the VB tail becomes occupied, and the CB edge becomes unoccupied, as shown in eqn (18) In this context, a 0 represents an Urbach absorption coefficient (constant), and E U , which stands for the Urbach energy, determines the slope of the exponential edge and can be seen as the width of the tail of localized states in the forbidden energy gap.The thermal vibrations of the lattice form the basis of the E U .The values of the E U and a 0 attained from the plots of ln a against hn in Fig. 11(a 19,46 The high density of localized states inside the E g , as implied by the enormous value of the E U , revealed numerous structural aws in the samples. 45e powerful probes, 12(a)) and surface 12(b)) energy loss functions depicting the electron and optical transitions in GDC ceramics.VELF and SELF are used to determine the energy loss rates of electrons as they move across most of the surface.The idiosyncratic peaks of VELF and SELF for GDC were observed at x3.3423, x3.1877, x3.2718, and x3.3333 eV. 45

Raman spectroscopy
CeO 2 exhibits a cubic uorite structure with a space group fm 3m (225), which has six optical phonon modes as per group theory; these modes correspond to the doubly degenerate transverse optical (TO) mode around 250 cm −1 , the triply degenerate Raman-active mode (F 2g ) around 465 cm −1 and the nondegenerate longitudinal optical (LO) mode around 600 cm −1 .TO and LO are infrared active modes.Fig. 13 shows the RT Raman spectra of GDC ceramics.The un-doped ceria (GDC-00) indicates only one sharp peak at 460 cm −1 .The peak at 460 cm −1 is assigned to the F 2g symmetric mode of stretching vibrations of O atoms around the Ce atoms (Ce-O bond). 37The F 2g mode is susceptible to any changes in the metal and oxide bond length or the generation of oxygen vacancies.However, GDC-20 shows one sharp peak around 460 cm −1 and two broad peaks around 560 and 600 cm −1 , with a smaller peak at 250 cm −1 .The dopant Gd reduces the intensity and increases the width of the F 2g peak.However, the peaks at x250 cm −1 , x560 cm −1 , and x604 cm −1 are due to the substitution of Ce by   Gd in the ceria uorite structure. 37This substitution generates oxygen vacancies within the uorite structure.The broad Raman band at x560 cm −1 appears because of the oxygen atom vibrating between Gd 3+ ions and Ce 4+ ions near oxygen vacancy defects.The Raman shi at x604 cm −1 originates from the vibration of oxygen atoms between Ce 4+ and Gd 3+ ions in the absence of oxygen defects. 37

Conclusions
Pure and Gd-doped ceria have been synthesized via sol-gel combustion; evidence of both pure CeO 2 and systems doped with Gd were supplied by the strong X-ray diffraction peaks that correspond to the reection planes (1 1 1), (2 2 0), (3 1 1), (2 2 2), (4 0 0), (3 3 1), (4 2 0), and (4 2 2).The produced GDC ceramic samples exhibited high crystallinity as seen by their low FWHM value and marked XRD peak intensity.Crystallographically, the synthesized GDC ceramics belong to the fm 3m (225) space group and feature a cubic architecture with a mono-phase.The computed d-interplanar spacings correlate well with the mentioned values; the SFs of GDC ceramics were determined.The C i of each XRD peak was used to gauge the s of crystallites along a crystal plane (h k l).The computed d h k l indicates that d 1 1 1 is dominant and h 1 1 1 is the lowest, indicating the importance of the GDC's (1 1 1) plane.Results from various methods for determining the GDC ceramic's microstructural parameters, including N-R, Scherrer, S-W, Monshi, W-S, W-H, SSP, and H-W, are consistent.The densities of GDC ceramics were determined using a pycnometer.As a result of Ce-O and Gd-O-Ce bonds, GDC exhibited broad peaks in the RT FTIR spectra at 1025, 897, 1131, and 952 cm −1 .The UV-vis-NIR spectrophotometer recorded the RT reectance (R) spectra of GDC ceramics.The spectra of a suggest that GDC shows two distinct peaks, one at the O-2p state of the VB and the other at the Ce-5d state of the CB.R-dependent refractive index (h), a-dependent extinction coefficient (k), and optical band gap (E g ) for the GDC-00, -10, -20, and -30 ceramic samples have been extracted.For GDC samples, the 3 i , 3 r , and tan d were computed close to l c .The results of the E U and a 0 calculations for the GDC ceramics are presented.s o and s e maxima and minima for GDC ceramics have been deduced.VELF and SELF were used to calculate the energy loss rates of electrons over the surface.Various vibrational modes in GDC ceramics were detected by Raman spectroscopy.

5 .
The Williamson-Hall (W-H) method.Despite considering the effects of D on the XRD peak broadening, the Scherrer method fails to explain lattice microstructures or intrinsic 3, which remains in powder form because of defects.Different effects on the line width are postulated to result from other D and 3 in the W-H method, which is why line broadening depends on the diffraction angle 2q.Since the broadening of the line can be attributable to either a Lorentzian or a Gaussian function, the values of D and 3 that were obtained are the median values of the line.Uniform deformation models (UDM) can be derived from the modied W-H equation, allowing for the measurement of D and microdeformation.
the charge carriers induced by the alternating the electric eld of the passing electromagnetic waves45 and were employed in investigating the electrical properties of different materials.As shown in Fig.11(b) and (c), the highest and lowest values of s 0 and s e for GDC-00, -10, -20, and -30 are x3.3423,x31 959, x3.2891, and x3.3514 eV for GDC-00, -10, -20, and -30, respectively.47

Fig. 9 E
Fig. 9 E g plot for GDC ceramics.

Fig. 10
Fig. 10 Variation in (a) IDC, (b) RDC, and (c) loss tangent as a function of energy for GDC ceramics.Fig. 11 (a) Urbach energy, (b) optical conductivity, and (c) electrical conductivity for GDC ceramics.

Table 4 E
g values for GDC ceramics